On the origins of mesospheric gravity waves

K. Sato,1 S. Watanabe,2 Y. Kawatani,2 Y. Tomikawa,3 K. Miyazaki,2 and M. Takahashi4

Received 8 July 2009; revised 24 August 2009; accepted 3 September 2009; published 7 October 2009.

[1] Using hourly data from a three-year simulation basedon a gravity-wave resolving general circulation model, wehave first inferred a global view of gravity wave sourcesand propagation affecting significantly the momentumbalance in the mesosphere. The meridional cross section ofmomentum fluxes suggests that there are a few dominantpropagation paths originating from the subtropics insummer and the middle to high latitudes in winter. Thesegravity waves are focused into the mesospheric jets in theirrespective seasons, acting effectively to decelerate the jets.The difference in the source latitudes likely contributes tothe hemispheric asymmetries of the jets. The horizontaldistribution of the momentum fluxes indicates that thedominant sources are steep mountains and troposphericwesterly jets in winter and vigorous monsoon convection insummer. The monsoon regions are the most importantwindow to the middle atmosphere in summer because of theeasterlies associated with the monsoon circulation.Citation: Sato, K., S. Watanabe, Y. Kawatani, Y. Tomikawa,

K. Miyazaki, and M. Takahashi (2009), On the origins of

mesospheric gravity waves, Geophys. Res. Lett., 36, L19801,

doi:10.1029/2009GL039908.

1. Introduction

[2] The wind around an altitude of 90 km in the uppermesosphere is always weak globally, indicating that the airat this level rotates at approximately the same speed as thesolid earth. This is a remarkable characteristic because thewind in the mesosphere below exhibits a dominant annualvariation, with a strong westerly jet in winter and easterly jetin summer, reflecting the latitudinal difference in absorptionof ultra-violet solar radiation by the ozone layer. Theoreticalwork in the early 1980s suggested that gravity waves werea possible physical justification for the artificial drag usedcommonly in numerical models to simulate the realisticpersistent weak wind layer in the upper mesosphere [Lindzen,1981;Matsuno, 1982]. Accurate estimates of the momentumflux associated with gravity waves at middle latitudes pro-vided by the Mesosphere-Stratosphere-Troposphere (MST)radars which were developed in the early 1980s supportedthis theoretical expectation [e.g., Tsuda et al., 1990]. Sincethen, our knowledge of gravity waves has been greatlyimproved through high-resolution observations by radars,

radiosondes and satellites, and gravity waves are nowrecognized as one of the essential components in the earthclimate system [e.g., Fritts and Alexander, 2003].[3] While some observations of gravity wave effects on

the mesosphere are possible, a global picture of gravity wavesources is presently beyond our reach. This is partly becausethe mesosphere is quite far from the source level in thetroposphere, and because the gravity waves inherently prop-agate in any direction. Current global climate models mustusually include gravity wave parameterizations becausegravity waves are usually sub-grid scale phenomena. Butthe gravity wave parameterizations still have a significantuncertainty in the formulations of the wave sources and takeaccount of only vertical wave propagation. The purpose ofthis study is to elucidate relative importance of varioussources of the gravity waves as a function of time and space,by examining their propagation to the mesosphere with ahigh-resolution global model. A comprehensive atmosphericgeneral circulation model with resolved gravity waves thatgives realistic results presumably has treated gravity wavescorrectly. Therefore, we can assume that the modelledeffects are a good surrogate for observations of the actualatmosphere.

2. Gravity-Wave Resolving GeneralCirculation Model

[4] We developed a high-resolution global spectral climatemodel to investigate seasonal and inter-annual variation ofglobal characteristics of small-scale phenomena includinggravity waves [Watanabe et al., 2008]; this has the followingadvantages. First, our model covers quite a wide height rangefrom the ground surface to the upper mesosphere. Second,our model resolution is T213 (triangular truncation at wave-number 213 corresponding to about 60 km) in the horizontaland 300 m in the vertical, which is almost sufficient to sim-ulate realistic propagation and momentum deposition ofgravity waves. Third, no gravity wave parameterizationsare included in our model, i.e., all gravity waves are internallygenerated. Fourth, the time integration was made over threemodel years in which a climatology with realistic seasonalvariation was specified for the sea surface temperature andstratospheric ozone. Physical quantities were sampled every1 hour.[5] Our preliminary analysis indicated that simulated

large-scale dynamical structures were quite realistic and thatgravity waves were essential for the momentum balance inthe upper mesosphere [Watanabe et al., 2008]. Using thismodel data, the tropopause and stratopause structure and theforcing of the QBO-like oscillation simulated spontaneouslywere examined by K. Miyazaki et al. (Transport and mixingin the extratropical tropopause region in a high verticalresolution GCM. Part I: Potential vorticity and heat budgetanalysis, submitted to Journal of Atmospheric Sciences,

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1Department of Earth and Planetary Science, University of Tokyo,Tokyo, Japan.

2Research Institute for Global Change, Japan Agency for Marine-EarthScience and Technology, Yokohama, Japan.

3National Institute of Polar Research, Tachikawa, Japan.4Center for Climate System Research, University of Tokyo, Kashiwa,

Japan.

Copyright 2009 by the American Geophysical Union.0094-8276/09/2009GL039908$05.00

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2009), Tomikawa et al. [2008], and Y. Kawatani et al. (Theroles of equatorial trapped waves and internal inertia-gravitywaves in driving the quasi-biennial oscillation. Part I: Zonalmean wave forcing, submitted to Journal of AtmosphericSciences, 2009), respectively. Upper mesospheric four-daywaves were analyzed byWatanabe et al. [2009]. The presentstudy examined a global view of the sources and propagationof mesospheric gravity waves using the model data.[6] Possible candidates for the sources of mesospheric

gravity waves include high mountains, jet streams, cyclones,fronts and convection mainly in the troposphere. Amongthem, radiation of gravity waves through adjustment pro-cesses resulting from spontaneous imbalance of large-scaleflows has recently received attention, though the details ofthis mechanism have not yet been explored theoretically[O’Sullivan and Dunkerton, 1995; Zhang, 2004; Plougonvenand Snyder, 2007; Sugimoto et al., 2008; Sato and Yoshiki,2008]. Even such spontaneous emission of gravity waves issimulated explicitly in our model.

3. Characteristics of the Momentum FluxesAssociated With Gravity Waves

[7] The most important physical quantity for examininggravity wave propagation is the vertical flux of zonal

momentum r0u0w0, where r0 is the basic atmosphericdensity, u0 and w0 are eastward and upward wind fluctua-tions, respectively, and the overbar represents a time and/orspatial average. The momentum flux is a good diagnostic

of gravity waves because it is conserved unless wavegeneration and/or dissipation occur [Eliassen and Palm,1961]. Although recently-available high-resolution satel-lite observations capture a global image of gravity wavesand provide useful information on the momentum flux inthe stratosphere [Ern et al., 2004; Alexander et al., 2008],it is hard to examine the wave propagation because of theobservational filter problem [Alexander, 1998].[8] Small horizontal-scale fluctuations with total wave-

number n greater than 22 (horizontal wavelengths ��1800 km) were designated as gravity waves. A time-latitude section of r0u0w0 associated with the gravitywaves is plotted in Figure 1a for the three model years at0.1 hPa (a height of about 64 km) in the mesosphere. Anannual cycle is clear, i.e., it is positive (negative) in summer(winter), which is consistent with radar observations atmiddle latitudes [Tsuda et al., 1990]. The positive summermaxima are located at lower latitudes (�30�) than thenegative winter maxima (�60�).[9] Figure 1b shows the result for 100 hPa (�16 km) in

the lower stratosphere, reflecting gravity wave source dis-tributions in the troposphere. A similar annual cycle in thesign of r0u0w0 to the mesosphere is evident, which is alsoconsistent with the MST radar observations [e.g., Sato,1994]. However, the latitudes of the maxima are significantlylower than those in the mesosphere. Negative winter maximaare observed around 35� and positive summer maxima arelocated around 10� in both hemispheres. The significantdifference in the maximum latitude suggests the latitudinalpropagation of gravity waves which is ignored in mostgravity wave parameterizations.[10] In order to see the paths of gravity wave propagation

from the lower stratosphere to the mesosphere, a meridionalcross section of r0u0w0 as well as mean zonal wind wasplotted in Figure 2a for July of the second year. Thewesterly jet in the winter (Northern) hemisphere is locatedaround 60�S and 50 km, and the easterly jet in the summer(Southern) hemisphere exhibits a slanted structure above50 km in the mesosphere. It is clear that the negative wintermaximum around 35�S and the positive summer maximumaround 10�N in the lower stratosphere are connected to themaxima in the mesosphere around 60�S and 30�N in theirrespective hemispheres. Similar paths were seen in theopposite season (i.e., January). It should also be addedthat there is another dominant path of gravity waves from70�S in the lower stratosphere to 60�S in the mesosphere,although the corresponding path was not seen in the NorthernHemisphere winter.[11] These characteristics of the momentum flux suggest

that gravity waves penetrating from the lower atmospheretend to be focused into the mesospheric jets in both seasons.Such focusing and vertical propagation of the waves deter-mine the latitudinal distribution of the momentum fluxconvergence. Thus the focusing acts effectively to decel-erate the mesospheric jets. It is also important to note thatthe hemispheric asymmetry of the mesospheric jets asobserved in Figure 2a may partly be attributable to thedifference in the source latitudes between the two seasons.For example, the gravity waves originating in the summersubtropical region propagate gradually to the higher lat-itudes, so that the mean wind deceleration occurs faster,namely, at lower altitudes at lower latitude regions. This

Figure 1. Time-latitude sections of momentum fluxassociated with gravity waves (colors) and zonal-meanwesterly winds (contours; in m s�1) (a) at 0.1 hPa in theupper mesosphere and (b) at 100 hPa in the lowerstratosphere.

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propagation feature may be significant in contributing tothe easterly jet structure leaning toward higher latitudes.

4. Meridional Propagation of Gravity Waves

[12] The wave focusing into the mesospheric jet can beexplained theoretically by the modification of the wave-number vector by the background fields. A ray-tracing theoryindicates that the time rate of change of the meridionalwavenumber l along the ray is proportional to the meridionalgradient of the background westerly wind U and the zonalwavenumber k:

dl

dt¼ �k @U

@y; ð1Þ

where we assume a sinusoidal wave structure proportionalto exp(kx + ly + mz � wt), t is time, x, y and z are thelongitudinal, latitudinal and vertical coordinates, and w isthe frequency relative to the ground [Jones, 1969]. Forsimplicity, the static stability is assumed to be constantlatitudinally. Linear theory shows that the direction of thehorizontal wavenumber vector (k, l) is equal to that ofhorizontal group velocity relative to the mean wind forgravity waves propagating energy upward. Because themean meridional wind is generally weak, it is considered

that the sign of l is equal to that of the meridional groupvelocity relative to the ground. Linear theory alsoindicates that gravity waves with negative k have negativer0u0w0. Thus, (1) means that the gravity waves havingnegative r0u0w0 tend to have negative (positive) l to thenorth (south) of the westerly jet. This is consistent with ageneral feature that the gravity waves with negative r0u0w0generated in the lower atmosphere are focused into themesospheric westerly jet in winter. Such wave focusinginto the westerly jet was discussed by Dunkerton [1984],and the importance of wavenumber modification byPreusse et al. [2002]. The focusing of gravity waveswith positive r0u0w0 into the easterly jet in summer is alsounderstood with this mechanism.[13] To confirm the wave focusing into the jet, a simple

ray tracing calculation was made for an idealized back-ground condition and simple initial wave parameters, so asto make its essence clear. A steady zonally-uniform westerlywind field that mimics the simulated (i.e., real) one inFigure 2a was given as the background field (thick con-tours in Figure 2b). The initial wave parameters given arepurely westward (eastward) wavenumber vectors in thewinter (summer) hemisphere as is consistent with the signof simulated r0u0w0, a typical horizontal wavelength of500 km, and a phase speed of zero relative to the ground.The gravity wave launch level was 2 km for the winterhemisphere and 8 km for the summer hemisphere, becausethe dominant wave sources are high mountains in winterand strong convection in summer, as shown later. Thincurves in Figure 2b show the results of the ray tracing. Thewave focusing into the jet is clear and consistent with themomentum flux distribution (Figure 2a). A slight change ofgiven initial wavelengths modifies the ray paths to somedegrees but not by much.

5. Origins of Gravity Waves PropagatingInto the Mesosphere

[14] Next, so as to see the dominant source regions ofgravity waves, the horizontal distribution of r0u0w0 at 100 hPain the lower stratosphere is examined. Figure 3 shows the

Figure 2. (a) A meridional cross section of momentumflux associated with gravity waves (colors) and zonal-meanwesterly winds (contours; in m s�1) in July. (b) Rays ofgravity waves (thin curves) in the idealized backgroundwesterly winds (thick contours in m s�1).

Figure 3. A horizontal map of momentum flux associatedwith gravity waves (colors) at 100 hPa in the lower strato-sphere. Red solid, red dashed, and black dashed contoursindicate zero, easterly, and westerly winds (in m s�1),respectively.

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result for July. It is clear that the distribution of r0u0w0 is notzonally uniform. In the Southern (winter) Hemisphere, largenegative values are observed at 100 hPa over high mountainssuch as the Andes at mid-latitudes and the Antarctic penin-sula at high latitudes. Thus, these are likely due to topo-graphically-forced gravity waves. In addition to theseisolated peaks, zonally-elongated negative r0u0w0 regionsare present in middle to high latitudes in the SouthernHemisphere. These are likely due to gravity waves sponta-neously emitted from strong westerly jets and fronts[O’Sullivan and Dunkerton, 1995; Kawatani et al., 2004;Zhang, 2004; Plougonven and Snyder, 2007; Tateno andSato, 2008].[15] In the Northern (summer) Hemisphere, positive

r0u0w0 values are dominant in the Indian and Africansummer monsoon regions. Thus, these are likely due togravity waves generated by strong convection in themonsoon regions. It is important that the mean wind in thisregion is easterly in the lower stratosphere associated withthe monsoon circulation, because it allows the eastward-propagating gravity waves to penetrate into the middleatmosphere.[16] Similar features are observed in January (not shown).

Dominant sources are the Rocky Mountains, mountains inEast Asia, and strong westerly jets in middle latitudes of theNorthern Hemisphere. Gravity waves in high latitudes of theNorthern Hemisphere are weak for lack of steep topography.Strong positive r0u0w0 is observed in the subtropical sum-mer monsoon regions in the Southern Hemisphere.

6. Summary and Concluding Remarks

[17] Using a high-resolution general circulation model,we examined the dominant sources and propagation of themesospheric gravity waves that affect significantly themomentum balance in the mesosphere. There were a fewdominant propagation paths to the mesosphere originatingin the subtropics in summer and in the middle to highlatitudes in winter in the lower stratosphere. These dom-inant gravity waves were focused into the mesosphericjets, which was attributable to the wavenumber modifica-tion by the jets themselves. The seasonal dependence of thesource latitudes likely plays an important role in accountingfor the hemispheric asymmetry of the mesospheric jets. Thefeatures of momentum fluxes in the lower stratosphereindicated that the dominant gravity wave sources are steepmountains and strong upper-tropospheric westerly jets inwinter and vigorous subtropical monsoon convection insummer. The monsoon regions were the most importantsource region in summer because of the easterlies in thelower stratosphere.[18] These results indicate that the latitudinal propagation

of gravity waves is important in determining the dynamicalstructure of the mesosphere, although it has been ignored inmost gravity wave parameterization schemes. An improve-ment of the gravity wave parameterizations by includingrelevant wave propagation and sources likely would lead tomore accurate, detailed and longer-term prediction of theweather and climate.[19] Although high-resolution global models are power-

ful to examine gravity waves in many aspects as discussedin this paper, the reality must be confirmed by observations

with similar or higher resolutions. In particular, our obser-vational knowledge in the polar regions is limited. Combi-nation of high-resolution models and observations with MSTradars and satellites will be promising for precise understand-ing of the global and detailed momentum balance.

[20] Acknowledgments. The authors are grateful to S. Tateno for hishelp of the data analysis and T. Tokioka and I. Hirota for their encourage-ment to perform this study. Our special thanks are due to D. G. Andrews forhis valuable comments and careful reading of the original manuscript.Thanks are also due to two anonymous reviewers for their constructivecomments. This study is supported by Grant-in-Aid for Scientific Research(A) 19204047 of the Ministry of Education, Culture, Sports and Technology(MEXT), Japan. The model simulation was conducted using the EarthSimulator. A part of the simulation was made as a contribution to theInnovative Program of Climate Change Projection for the 21st Centurysupported by MEXT.

ReferencesAlexander, M. J. (1998), Interpretations of observed climatological patternsin stratospheric gravity wave variance, J. Geophys. Res., 103, 8627–8640.

Alexander, M. J., et al. (2008), Global estimates of gravity wave momen-tum flux from High Resolution Dynamics Limb Sounder observations,J. Geophys. Res., 113, D15S18, doi:10.1029/2007JD008807.

Dunkerton, T. J. (1984), Inertia-gravity waves in the stratosphere, J. Atmos.Sci., 41, 3396–3404.

Eliassen, A., and E. Palm (1961), On the transfer of energy in stationarymountain waves, Geofys. Publ., 22, 1–23.

Ern, M., P. Preusse, M. J. Alexander, and C. D. Warner (2004), Absolutevalues of gravity wave momentum flux derived from satellite data,J. Geophys. Res., 109, D20103, doi:10.1029/2004JD004752.

Fritts, D. C., and M. J. Alexander (2003), Gravity wave dynamics andeffects in the middle atmosphere, Rev. Geophys., 41(1), 1003, doi:10.1029/2001RG000106.

Jones, W. L. (1969), Ray tracing for internal gravity waves, J. Geophys.Res., 74, 2028–2033.

Kawatani, Y., M. Takahashi, and T. Tokioka (2004), Gravity waves aroundthe subtropical jet of the southern winter in an atmospheric generalcirculation model, Geophys. Res. Lett., 31, L22109, doi:10.1029/2004GL020794.

Lindzen, R. S. (1981), Turbulence and stress owing to gravity wave andtidal breakdown, J. Geophys. Res., 87, 9707–9714.

Matsuno, T. (1982), A quasi one-dimensional model of the middle atmo-sphere circulation interacting with internal gravity waves, J. Meteorol.Soc. Jpn., 60, 215–226.

O’Sullivan, D., and T. J. Dunkerton (1995), Generation of inertia-gravitywaves in a simulated life cycle of baroclinic instability, J. Atmos. Sci., 52,3695–3716.

Plougonven, R., and C. Snyder (2007), Inertia-gravity waves spontaneouslygenerated by jets and fronts. Part I: Different baroclinic life cycles,J. Atmos. Sci., 64, 2502–2520.

Preusse, P., et al. (2002), Space-based measurements of stratospheric moun-tain waves by CRISTA, 1, Sensitivity, analysis method, and a case study,J. Geophys. Res., 107(D23), 8178, doi:10.1029/2001JD000699.

Sato, K. (1994), A statistical study of the structure, saturation and sourcesof inertio-gravity waves in the lower stratosphere observed with the MUradar, J. Atmos. Terr. Phys., 56, 755–774.

Sato, K., and M. Yoshiki (2008), Gravity wave generation around the polarvortex in the stratosphere revealed by 3-hourly radiosonde observationsat Syowa Station, J. Atmos. Sci., 65, 3719 – 3735, doi:10.1175/2008JAS2539.1.

Sugimoto, N., K. Ishioka, and K. Ishii (2008), Parameter sweep experi-ments on spontaneous gravity wave radiation from unsteady rotationalflow in an f-plane shallow water system, J. Atmos. Sci., 65, 235–249.

Tateno, S., and K. Sato (2008), A study of inertia-gravity waves in the middlestratosphere based on intensive radiosonde observations, J. Meteorol. Soc.Jpn., 85, 719–732.

Tomikawa, T., K. Sato, S. Watanabe, Y. Kawatani, K. Miyazaki, andM. Takahashi (2008), Wintertime temperature maximum at the subtro-pical stratopause in a T213L256 GCM, J. Geophys. Res., 113, D17117,doi:10.1029/2008JD009786.

Tsuda, T., Y. Murayama, M. Yamamoto, S. Kato, and S. Fukao (1990),Seasonal variation of momentum fluxes in the mesosphere observed withthe MU radar, Geophys. Res. Lett., 17, 725–728.

Watanabe, S., Y. Kawatani, Y. Tomikawa, K. Miyazaki, M. Takahashi, andK. Sato (2008), General aspects of a T213L256 middle atmosphere gen-eral circulation model, J. Geophys. Res., 113, D12110, doi:10.1029/2008JD010026.

L19801 SATO ET AL.: ORIGINS OF MESOSPHERIC GRAVITY WAVES L19801

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Watanabe, S., Y. Tomikawa, K. Sato, Y. Kawatani, K. Miyazaki, andM. Takahashi (2009), Simulation of the eastward 4-day wave in theAntarctic winter mesosphere using a gravity wave resolving generalcirculation model, J. Geophys. Res., 114, D16111, doi:10.1029/2008JD011636.

Zhang, F. (2004), Generation of mesoscale gravity waves in upper-tropo-spheric jet-front systems, J. Atmos. Sci., 61, 440–457.

�����������������������Y. Kawatani, K. Miyazaki, and S. Watanabe, Research Institute for

Global Change, Japan Agency for Marine-Earth Science and Technology,Yokohama 236-0001, Japan.

K. Sato, Department of Earth and Planetary Science, University ofTokyo, Tokyo 113-0033, Japan. (kaoru@eps.s.u-tokyo.ac.jp)M. Takahashi, Center for Climate System Research, University of Tokyo,

Kashiwa 277-8568, Japan.Y. Tomikawa, National Institute of Polar Research, Tachikawa 190-8518,

Japan.

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